When one element of a workpiece is to be welded to another element of that workpiece, it frequently is desirable to form a continuous weld of three hundred and sixty degrees angular extent at the joint between those two elements; and the patented welder can provide such a weld where either of those elements can be rotated through three hundred and sixty degrees. However, some workpieces have forms and configurations which preclude their rotation through three hundred and sixty degrees while those workpieces are mounted in a welding machine. In fact, workpieces are known which can be rotated only through two hundred and seventy degrees while they are mounted in a welding machine. Although it would be possible to provide a three hundred and sixty degree weld at the point between two elements of such a workpiece, by successively mounting that workpiece in two different positions in the patented welder, that weld would not be homogeneous. Also, valuable time would be required to successively mount that workpiece in those two different positions.